The product of frequency and wavelength is equal to the velocity of light because of the fundamental nature of electromagnetic waves.
An electromagnetic wave, such as light, is characterized by its frequency (f) and wavelength (λ). Frequency represents the number of oscillations or cycles of the wave that occur per unit of time, while wavelength represents the distance between two corresponding points on the wave (such as two adjacent peaks or troughs).
The velocity of light (c) is a constant in a given medium, such as vacuum or air, and it represents the speed at which light propagates through that medium. In vacuum, the velocity of light is approximately 299,792,458 meters per second (m/s).
The relationship between frequency, wavelength, and velocity of light can be expressed by the following equation:
c = f × λ
Where: c = velocity of light f = frequency of the wave λ = wavelength of the wave
This equation, known as the wave equation, shows that the product of frequency and wavelength is equal to the velocity of light. It means that as the frequency of a wave increases, its wavelength decreases, and vice versa, while the velocity of light remains constant. This relationship holds true for all electromagnetic waves, including light.